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Extinction and Persistent of a Stochastic Multi-group SIR Epidemic Model
Xiaojing Zhong and Feiqi Deng
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DOI:10.17265/2328-2231/2013.12.002
Systems Engineering Institute, South China University of Technology, Guangzhou 510640, P.R. China
We establish a stochastic differential equation epidemic model of multi-group SIR type based on the deterministic R0S multi-group SIR mode. Then, we define the basic reproduction number and show that it is a sharp threshold for the dynamic of R0S the stochastic multi-group SIR model. More specially, if < 1, then the disease-free equilibrium will be asymptotically stable R S which means the disease will die out, if 0 > 1, the disease-free equilibrium will unstable, and our model will positively recurrence to a positive domain which implies the persistence of our model. Numerical simulation examples are carried out to substantiate the analytical results.
Stochastic, multi-group SIR model, threshold dynamics, positive recurrence, stochastic persistence
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